The Gravitron single-car roller coaster consists of a single loop-the-loop. The

Question

The Gravitron single-car roller coaster consists of a single loop-the-loop. The car is initially pushed, giving it just the right mechanical energy so the riders on the coaster will feel “weightless” when they pass through the top of the circular arc. How heavy will they feel when they pass through the bottom of the arc (that is, what is the normal force pressing up on them when they are at the bottom of the loop)? Express the answer as a multiple of mg (their actual weight). Assume any effects of friction or of air resistance are negligible.

Explanation / Answer

at the top of loop,

in vertical,

mg - N = m*a_c

a_c = centripetal force = v^2 / r

mg - N = mv^2 /r

N = mg - mv^2 /r

if at top weighless is felt that means N = 0

mv^2 / r = mg

at bottom,

N - mg = mac = mv^2 / r

N = mg + mv^2/r

and mv^2 /r = mg

so N = mg + mg = 2mg

at bottom 2mg heavy will be felt.

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